Exporting obj file with separate parts
CORRECTED FIX: The problem was my Blender export settings. To ensure DAZ gets the normals correct on all faces, you need these settings: where (+) means checked and (-) means unchecked -- and they worked:

Forward (Z Forward), Up (Y Up), Selection Only (-), Animation (-), Apply Modifiers (+), Include Edges (+), Smooth Groups (-), Bitflag Smooth Groups (-), Write Normals (+), Include UVs (+), Write Materials (+), Triangulate Faces (-), Write Nurbs (-), Polygroups (-), Objects as OBJ Objects (-), Objects as OBJ Groups (+), Material Groups (-), Keep Vertex Order (-), Scale (100.00), Path Mode (Auto).